Static and Dynamic Tearing of Thin Steel Sheets

This paper presents the energy analysis of static mode III fracture of thin steel sheets. For dynamic tearing studies we used the Charpy test apparatus. Static tearing tests performed on three types of steel sheets indicate that the linear relationship of Mai and Cotterell is valid for specimens with a leg width W up to 30 mm. In the given range, the specific work of fracture _e is determined according to the Mai–Cotterell model. The _e kinetics is studied as a function of the sheet thickness B, radius of curvature , and loading rate V. The modified model includes a linear dependence of versus W. Moreover, we show that variation of the loading rate V from 1 to 300 mm/min has no effect on the specific work of fracture _e. A slight decrease in the dynamic fracture toughness J_0,d has been found.     

Analytical Theory of DC SQUIDS Operating in the Presence of Thermal Fluctuations

A comprehensive analytical theory of symmetric DC SQUIDs is presented taking into account the effects of thermal fluctuations. The SQUID has a reduced inductance < 1/ where = 2LI_c/₀, L is the loop inductance, ₀ is the flux quantum, and I_c is the critical current of the identical Josephson junctions which are assumed to be overdamped. The analysis, based on the two dimensional Fokker–Planck equation, has been successfully performed in first order approximation with considered a small parameter. All important SQUID characteristics (circulating current, current-voltage curves, transfer function, and energy sensitivity) are obtained. In the limit 1( = 2k_BT/I_c0 is the noise parameter, k_B is the Boltzmann constant, and T is the absolute temperature) the theory reproduces the results of numerical simulations performed for the case of small thermal fluctuations. It was found that for < 1 the SQUID energy sensitivity is optimum when is higher than 1/, i.e., outside the range for which the present analysis is valid. However, for 1 the energy sensitivity has a minimum at L = L_F , where L_F = ( ₀ /2) ²/k_B , and therefore, in this case, the optimal reduced DC SQUID inductance is _opt = 1/, i.e., within the range for which the present analysis is valid. In contrast to the case of an RF SQUID, for a DC SQUID the transfer function decreases not only with increasing L/L_F but also with increasing (as 1/). As a consequence, the energy sensitivity of a DC SQUID with < 1/ degrades more rapidly (as ⁴ ) with the increase of than that of an RF SQUID does (as ² ).     

Theory of RF SQUIDs Operating in the Presence of Large Thermal Fluctuations

A comprehensive analytical theory is presented for non-hysteretic RF SQUIDs operating in the adiabatic mode in the presence of large thermal fluctuations. When 1 ( = 2LI_c/₀ is the hysteresis parameter, L is the SQUID inductance, I_c is the critical current of the Josephson junction, and ₀ is the flux quantum) the theory is applicable also for RF SQUIDs operating in the non-adiabatic mode. In contrast to previous theories in which the noise is treated perturbatively and which therefore are applicable only if the product 1 ( = 2k_BT/ ₀ I_c is the noise parameter, k_B is the Boltzmann constant, and T is the absolute temperature)—the case of small thermal fluctuations—the present theory is valid for around unity or higher. In the limit 0 the theory reproduces the results of small thermal fluctuations theories. It has been found that in the presence of large thermal fluctuations the screening current in the SQUID inductance is suppressed by a factor that increases with increasing . Taking into account this new basic fact, all SQUID characteristics (output signal, transfer function, noise spectral density and energy sensitivity) have been recalculated and a good agreement with experimental data has been obtained. It has been also found that RF SQUIDs can be operated with substantially higher values of the inductance and of the noise parameter than DC SQUIDs. These two aspects, which are of particular importance at liquid nitrogen temperature, make high T_c RF SQUIDs very attractive.     

Kohn-luttinger effect and the instability of a repulsive Fermi-liquid at T=0

I consider the possibility for a pairing instability in a 2D repulsive Fermi-liquid due to the singularity in the scattering amplitude (q) at the momentum transfer q 2p_F (Kohn-Luttinger effect). For arbitrary Fermi-liquid, (q) for the particles at the Fermi surface is found to have a singular part, ^sing(q) . For large 2D orbital momentum l, this term gives a dominant attractive contribution to the scattering amplitude and leads to a pairing instability in a 2D Fermi-liquid with arbitrary short-range repulsion. In the dilute limit, numerical studies show that the effect survives down to l=1 and gives rise to a p-wave pairing.     

Thermal response of a3He-superfluid-4He mixture

The response of a layer of superfluid mixture to an ac heat source,Q(t)=Q ₀ exp(it), is determined. In the low-frequency regime, the temperature response at the heated side of a superfluid layer is essentially identical to that of an ordinary fluid having a thermal conductivity _eff and a thermal diffusion coefficient ₀ /2. Here _eff is the effective conductivity of Khalatnikov, and ₀ is the diffusion coefficient of Griffin. At much higher frequencies, the results are more complicated. The low-frequency regime is defined in terms of the second sound velocityu ₂ by u ₂ ² / ₀ . The ac response function is valuable in a number of ways. It can be used to obtain the system response to more complicated time-dependent variations inQ such as step changes inQ. A knowledge of the response function in the low-frequency regime provides a mechanism for directly determining the Kapitza resistance in mixtures. Finally, a knowledge of the response function provides an additional opportunity to test two-fluid hydrodynamics. Alternative tests of superfluid hydrodynamics are of particular interest in light of recent experiments that show anomalous values for _eff in the low ³ He concentration limit     

Tilted and Crossing Vortex Chains in Layered Superconductors

No Heading In presence of the Josephson vortex lattice in layered superconductors, small c-axis magnetic field penetrates in the form of vortex chains. In general, structure of a single chain is determined by the ratio of the London [] and Josephson [_J] lengths, = /_J. The chain is composed of tilted vortices at large s (tilted chain) and at small s it consists of crossing array of Josephson vortices and pancake-vortex stacks (crossing chain). We study chain structures at the intermediate s and found two types of phase transitions. For 0.6 the ground state is given by the crossing chain in a wide range of pancake separations a [2–3]_J. However, due to attractive coupling between deformed pancake stacks, the equilibrium separation can not exceed some maximum value depending on the in-plane field and . The first phase transition takes place with decreasing pancake-stack separation a at a = [1 – 2]_J, and rather wide range of the ratio , 0.4 0.65. With decreasing a, the crossing chain goes through intermediate strongly-deformed configurations and smoothly transforms into the tilted chain via the second-order phase transition. Another phase transition occurs at very small densities of pancake vortices, a [20 – 30]_J, and only when exceeds a certain critical value 0.5. In this case small c-axis field penetrates in the form of kinks. However, at very small concentration of kinks, the kinked chains are replaced with strongly deformed crossing chains via the first-order phase transition. This transition is accompanied by a very large jump in the pancake density.PACS numbers: 74.25.Qt, 74.25.Op, 74.20.De     

Transient two-dimensional diffusion along a high-diffusivity lamina which bisects a half-space

Summary The right half-space is bisected by a high-diffusivity planar sheet which lies along the x-axis. A sudden increase in the potential on (y-axis) causes longitudinal diffusion along coupled with transverse diffusion from into . Restricting to the case of large diffusivity ratio, to , it is demonstrated that the problem possesses a sequence of three distinct time domains in which self-similar solutions become asymptotically valid. The early, intermediate, and late solutions are each functions of only two independent variables; they are universally valid for all parameter values; and they are easily computed and readily applied. Transitions between asymptotics are described by expansions in time, the perturbations being regular in the early-intermediate period but singular in the intermediate-late period. The considered problem is a linear example which affords the opportunity for comparison with Fourier-Laplace analysis, and has application to thermal or electric conduction, diffusion mass transfer, and Darcy-flow of fluid in a fractured or layered porous medium. Methodology and qualitative observations are applicable to more complex nonlinear problems of the same class.This work supported by the U.S. Department of Energy under Contract DE-ACO4-76D00789.A U.S. DOE Facility.     

Pseudogap and Transport in HTS

Perpendicular transport is one of the key factors to HTS superconductivity, sampling the quasi-insulating blocking layer, separating the conducting CuO-planes, and driving the metal–insulator transition (MIT) that is induced by disorder and underdoping. Various measurements have been carried out to study the transport, the MIT, and the in-plane Fermi surface especially by surface methods via the blocking layer, and these depend sensitively on surface quality. ARXPS results on UHV cleaving show that at 300 K and 10^–10 Torr, a Bi hydroxide layer occurs in 30 min, followed by H₂O or C_y H_x OH chemisorption. Consequences of this result on STS, ARPES, perpendicular transport, Coulomb charging, and pseudogap are analyzed, yielding scenario for HTS superconductivity, where static and dynamic charge exchange via and with the blocking layer initiates plaques of preformed pairs of d-wave symmetry weakening the inplane Coulomb repulsion yielding by this plasmonic mechanism, finally, HTS. Consequences of this scenario on anisotropic transport with its strong Fermi velocity v_F anisotropy and its strong in-plane scattering rate (T) const. at (, 0) in k-space with pseudo gap kT^* _{_P}/3 and superconducting gap _S 3 kT_c maxima and the strongly decreasing rate (T) T at 0.4 (, ) with pseudo gap _{_p} (k) node and superconducting gap _s (k node are given.     

Magnetic field dependence of zero-sound attenuation close to the pair-breaking edge in3He-B due toJ=1−,J z =±1 collective modes

Our previous theory yielded for the Zeeman splitting of the imaginaryJ=1 collective mode in³He-B the result =2+0.25J _z ( is the effective Larmor frequency). In this paper we take into account the downward shift of the pair-breaking edge from 2 to 2₂– (₂ and ₁ are the longitudinal and transverse gap parameters). This leads to a complex Landé factor: the frequencies of theJ _z =±1 components become =2+0.39J _z , and the linewidths of these resonances become finite: =0.18. The coupling amplitudes of theJ _z =±1 components to density are found to be proportional to gap distortion, (₁–₂/(/)². Our results for the ultrasonic attenuation due to theJ _z =±1,J=1 modes are capable of explaining the field dependence of the attenuation close to the pair-breaking edge as observed by Dobbs, Saunders, et al. The observed peak is caused by theJ _z =–1 component: its height increases due to gap distortion as the field is increased, and the peak shifts downward in temperature and its width increases with the field due to the complex Landé factor. TheJ _z =+1 component gives rise to a corresponding dip relative to the continuum attenuation.     

The Electrical Conductivity of a Fully Ionized Magnetic Plasma with Screened Interaction between Charges

The method of solving the kinetic Boltzmann equation is used to calculate the electrical conductivity of a fully ionized plasma with screened interaction between charges, located in a time-constant external magnetic field. The dependence of the longitudinal, transverse, and Hall conductivity on the nonideality parameter of the plasma and on the parameter _{e 0} is established. It is demonstrated that the maximum (modulo) value of the Hall components of plasma conductivity shifts towards lower values of the intensity H of external magnetic field as the nonideality parameter increases.     

The dielectric properties of glass-ceramic-on-metal substrates for microelectronics packaging

The dielectric properties of some glass-ceramic-on-metal substrates have been determined over the frequency range 500 Hz to 5 MHz using a.c. bridge techniques. The substrates consisted of cordierite-based glass-ceramics screen printed on molybdenum. For glass layers of thickness greater than 100 m both the permittivity, and the dielectric loss, , are frequency independent over this frequency range at room temperature giving the value of =6.5 and tan =8×10^–3; the room-temperature data are consistent with the universal law of dielectric response. The variation of permittivity with temperature has also been examined and, below 120 °C, the temperature coefficient [(–1) (+2)]^–1 (/T)_p, was found to be 1.3×10^–5 K^–1. The results are compared with those previously reported for Al₂O₃ and AIN substrates.     

Angular Dependence of the Activation Energy in YBCO/PBCO Multilayers

The activation energy in several (YBCO) _m /(PBCO) _n superconducting multilayers was deduced from resistivity measurements in magnetic fields up to 16 T, as a function of the angle between the magnetic field and the ab planes. The activation energy U ₀ (B,) scales with a reduced field B _red =B(sin ² +cos ² / ² ) ^1/2 , with an angle dependent anisotropy parameter . A crossover from U ₀ log B _red , at low B _red , to U ₀ (B _red ) at high B _red , is also observed. The implications of these results on vortex dynamics and on the coupling between the superconducting layers will be discussed.     

Effect of resonant impurity scattering on collective mode peaks in the ultrasound attenuation of heavy fermion superconductors

We have calculated the attenuation of longitudinal ultrasound due to real order parameter fluctuations in impure polar and planarp-wave superconductors. The quasiparticle self-energy and the corresponding vertex corrections have been included in thet-matrix approximation for arbitrary scattering rate =1/2_N and all scattering phase shifts _N (0 _N/2). We obtain sound attenuation peaks belowT _c whose heights, positions, and shapes depend on ₀ (sound frequency), (₀), _N, and (coupling strength due to particle-hole asymmetry). The peaks become much more distinct and sharper for _N =/2 (resonant scattering by impurities) than for _N=0 (Born approximation). By choosing , _N, and suitably, qualitative agreement between calculated and observed peaks in UBe₁₃ and UPt₃ can be achieved.     

Intensity of critical opalescence of helium-4

We present measurements of the critical opalescence of helium-4. The results are analyzed by the Einstein and Ornstein-Zernike theory and the power laws. We obtain ==1.17±0.02, ==0.62±0.1,/=4.5±0.3,P _c =1706.008 mm Hg, andT _c =5,189.863 mK (T ₅₈ ). The critical behavior of helium-4 is almost the same as that of classical fluids and the influence of the quantum nature of helium-4 is not as evident as has been claimed.     

Antiferromagnetic ordering of enhanced nuclear spin in Cs2NaHoCl6

The field dependence of the magnetic susceptibility at low temperatures was investigated in a single crystal of Cs₂NaHoCl₆. The result is well explained by the second-order Zeeman splitting of the electronic ground state with a nonmagnetic ₃ doublet. Enhanced nuclear cooling experiments were carried out. Antiferromagnetic ordering of the enhanced nuclear spin system was observed at about 1.5 mK.     

Properties of r.f. sputtered cadmium telluride thin films

CdTe thin films were prepared using r.f. magnetron sputtering in an Ar atmosphere. Substrate temperatures in the range 100–320 °C were used. XRD results showed that the films are amorphous below 200 °C while above 200 °C the firms were polycrystalline with cubic structure and grains preferentially oriented along the [1 1 1] crystallographic direction. SEM measurements showed significant enhancement of crystallite size with increase of T _s or with post-preparation annealing above 400 °C. The 5 K photoluminescence spectrum showed a broad (FWHM=80 meV) band with a maximum at 1.538 eV. This band showed significant narrowing after annealing above 400 °C suggesting that it originates from transitions involving grain boundary defects. The refractive index n was determined from the interference pattern of the optical transmission. The results agree with the values of n calculated using the Jensen theory. The absorption coefficient was determined for photon energies hE _g (the energy bandgap) from the optical transmission spectra in the absorption region using the Swanepoel theory. Several direct and indirect allowed optical transitions were identified. It was found that the transitions can be grouped into four main allowed transitions (two direct; E _o, E ₃ and two indirect; E ₁, E ₂) whose energy values vary from one sample to another due the quantum size effect associated with small grain size. The main transitions are: E _o (1.50–1.77 eV) assigned to ₈ valence band (VB)₆ conduction band (CB) transition, E ₁ (1.84–2.05 eV) assigned to L_4,5(VB) _i transition where _i is an impurity level at 1.2 eV above the ₈ (VB), E ₂ (2.37–2.49 eV) assigned to L_4,5 (VB)₆ (CB) transition and E ₃ (2.25–2.55 eV) assigned to ₇ (VB) _i transition. The impurity is attributed to native centers or grain-boundary-related defects.     

Turbulent mixing of fluids with different densities flowing through a pipe

A one-dimensional model of a disperse mixture in a turbulent stream is constructed, with the mutual effect of mixture concentration and turbulence intensity taken into account.Notation ₀ mean-over-the-section density - p pressure - _t turbulent viscosity - U average longitudinal velocity - g acceleration of gravity - angle of pipe inclination from the horizontal - x, r cylindrical coordinates - t time - V average radial velocity - C average concentration - D_t turbulent diffusivity - c₀ mean-over-the-section concentration - K effective turbulent diffusivity - U₀ mean flow velocity - X distance, in the moving system of coordinates - a pipe radius - ₀ frictional stress at the inside surface of the pipe - u_* transient turbulent velocity - b turbulence intensity - l linear scale factor - chemical potential of mixture - density of mixture - d₁, d₂ densities of homogeneous fluids - y₊ thickness of laminar layer - y distance from the inside pipe surface - ₊ derivative of velocity at the layer boundary on the turbulent side - hydraulic drag - Gr Grashof number - Re Reynolds number - ₁, ₂, coefficients in the equation for K_* - K_* dimensionless effective diffusivity - =U₀t/2a dimensionless time - =X/2a dimensionless distance Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 6, pp. 992–998, June, 1972.     

Dynamics of Trapped Bose Gases at Finite Temperatures

Starting from an approximate microscopic model of a trapped Bose-condensed gas at finite temperatures, we derive an equation of motion for the condensate wavefunction and a quantum kinetic equation for the distribution function for the excited atoms. The kinetic equation is a generalization of our earlier work in that collisions between the condensate and non-condensate (C ₁₂ ) are now included, in addition to collisions between the excited atoms as described by the Uehling–Uhlenbeck (C ₂₂ ) collision integral. The continuity equation for the local condensate density contains a source term ₁₂ which is related to the C ₁₂ collision term. If we assume that the C ₂₂ collision rate is sufficiently rapid to ensure that the non-condensate distribution function can be approximated by a local equilibrium Bose distribution, the kinetic equation can be used to derive hydrodynamic equations for the non-condensate. The ₁₂ source terms appearing in these equations play a key role in describing the equilibration of the local chemical potentials associated with the condensate and non-condensate components. We give a detailed study of these hydrodynamic equations and show how the Landau two-fluid equations emerge in the frequency domain is a characteristic relaxation time associated with C ₁₂ collisions. More generally, the lack of complete local equilibrium between the condensate and non-condensate is shown to give rise to a new relaxational mode which is associated with the exchange of atoms between the two components. This new mode provides an additional source of damping in the hydrodynamic regime. Our equations are consistent with the generalized Kohn theorem for the center of mass motion of the trapped gas even in the presence of collisions. Finally, we formulate a variational solution of the equations which provides a very convenient and physical way of estimating normal mode frequencies. In particular, we use relatively simple trial functions within this approach to work out some of the monopole, dipole and quadrupole oscillations for an isotropic trap.     

Dynamic Measurements of Thermal Transport Coefficients and Boundary Resistance. II.Model for 3He-Superfluid 4He Mixtures

This is the second of a three-part study of the ac response of liquid helium. We derive the temperature response function, T(), of a ³ He-superfluid ⁴ He mixture from the equations of superfluid hydrodynamics in the presence of two interfacial boundary resistances,R_b.Specifically, we consider the response T(), across a fluid layer of thickness,d, to an ac heat flux,Q(t) = Q_o exp(it).T() depends on the effective thermal conductivity, _eff , Griffin's diffusion coefficient, _o (i.e. the thermal diffusivity of ³ He impurities, D_iso in the low ³ He concentration limit) and the thermal boundary resistance, 2R_b. This analysis provides the basis for experiments to determine these parameters. Although past experiments to measure these properties have been carried out using dc and transient techniques, an ac technique offers significant noise reduction over these techniques. By sweeping the frequency, it is possible for an experimenter to clearly identify different components of the system response to the heat flux. For instance, if t is the slowest fluid thermal response time, conventional Kapitza boundary effects dominate at frequencies, 1. These calculations reveal an interesting analogy to the Piston Effect for near-critical classical fluids. In Part I of this work, we used normal liquid ⁴ He as a testing ground for developing models of ac heat transport. In Part III of this work, we will present results in which we apply this technique to measurements on dilute mixtures of ³ He in superfluid ⁴ He.     

Theoretical analysis of the basic parameters of ultrasonic flowmeters

Conclusions A comparison of the final results of the two methods shows that the analytical expressions for the interchannel phase difference and repetition frequency difference F, and in the case of pulsed circuits also of the pulse propagation time difference , differ in the two methods by their corrections B and B.Errors in using the analytical expressions obtained by the approximate method do not exceed 1% when the hydrodynamic correction B for b_n0.1 is applied. If this value is taken as the basic error, the application of the approximate method is justifiable for pipe diameters exceeding 200 mm with piezoelectric element radii of r10 mm, and for pipe diameters exceeding 100 mm with element radii of r5 mm. Therefore, the application of the approximate method is limited in the main to the range of pipes with large and to a certain extent medium diameters. For the greater part of pipes with medium diameters and those with small diameters, it is necessary to use the analytical expressions obtained by the rigorous method. The use of these equations is also required for pipes with large diameters in designing high-precision flowmeters.